Chop walnuts and in a small skillet cook in oil over moderate heat, stirring, until lightly toasted. Cool nuts slightly.
Preheat broiler.
Coarsely grate apple and finely chop dates. In a bowl stir together all ingredients except pitas until combined well.
Horizontally split pitas and arrange, cut sides down, on a large baking sheet. Broil pitas about 4 inches from heat until golden and crisp, 1 1/2 to 2 minutes. Remove baking sheet from oven and turn pitas over. Divide Cheddar mixture among pitas, spreading evenly. Broil pitas until cheese mixture begins to bubble, about 2 minutes. Cut each pita into 6 wedges.
